Finite Group Databasebeta

← #19212239

Subgroups — #19212239

Order 5888.

606 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10625101C211yesmaximal, characteristic
2C4×C22⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
3#15671219C212yesmaximal, complemented
4#15671217C212yesmaximal, complemented
5C23×#1817C211yesmaximal, characteristic, complemented
6C2×#10625101C411yescharacteristic
7C2×C4×D92C411yescharacteristic
8C2×C4×C22⋊D23—21no—
9C2×C22⋊(C23⋊C8)—21no—
10C2×C4×C23⋊C8—21no—
11#13092319C2211yescharacteristic
12#13092315C2211yescharacteristic
13#13092308—21no—
14#13092296—21no—
15#13092277C411yescharacteristic
16C4×C4⋊Dic23C411yescharacteristic
17C4×(C2×D23)⋊C4—21no—
18#13092172C2212yes—
19C22×C42×C23C2211yescharacteristic
20C2×C23×C22⋊C8—21no—
21C23×#336—21no—
22C23×#336C2212yes—
23C23×C4×C23C2×C411yescharacteristic
24C23×C4×C23D411yescharacteristic
25C23×C4×C23D411yescharacteristic
26C22×C22⋊D23—21no—
27C22×D92C2×C411yescharacteristic
28C22×C4×D23—21no—
29C22×C8×C23—22no—
30C2×C42×C23—42no—
31C2×C42×C23C2×C411yescharacteristic
32C2×C42×C23D411yescharacteristic
33C2×C42×C23D411yescharacteristic
34C2×C42×C23C2311yescharacteristic
35C2×C22⋊Dic23—21no—
36#10625101—22no—
37#10625101C814yescomplemented
38C4×C22⋊D23—44no—
39C2×(C2×D23)⋊C4—21no—
40C2×(C2×D23)⋊C4—21no—
41C2×(C2×D23)⋊C4—21no—
42C2×(C2×D23)⋊C4—21no—
43C2×C4⋊Dic23C2×C411yescharacteristic
44C2×C4⋊Dic23C2×C411yescharacteristic
45C2×C4⋊Dic23C2×C411yescharacteristic
46C2×Dic23⋊C4—21no—
47C2×C4×Dic23—21no—
48C22×C23⋊C8—22no—
49C4×D92—42no—
50C23×C22⋊C8—42no—
51C23⋊#95—21no—
52C23⋊#95—21no—
53C23⋊#95—21no—
54C22⋊(C23⋊C8)—24no—
55C4×C23⋊C8—42no—
56C24×C23C22⋊C411yescharacteristic
57C23×D23—21no—
58C22×C4×C23—22no—
59C22×C4×C23—22no—
60C22×C4×C23—22no—
61C22×C4×C23—22no—
62C22×C4×C23—41no—
63C22×C4×C23—41no—
64C22×C4×C23—41no—
65C22×C4×C23—41no—
66C22×C4×C23C22⋊C411yescharacteristic
67C22×C4×C23C22⋊C411yescharacteristic
68C22×C4×C23C22⋊C411yescharacteristic
69C22×C4×C23C2×C812yes—
70C22×C4×C23M1612yes—
71C22×C4×C23C22×C411yescharacteristic
72C22×C4×C23C2×D411yescharacteristic
73C22×C4×C23C2×D411yescharacteristic
74C2×C22⋊D23—24no—
75C2×C22⋊D23—42no—
76C2×C22⋊D23—42no—
77C22×Dic23—21no—
78C22×Dic23—21no—
79C22×Dic23—21no—
80C2×D92—21no—
81C2×D92—41no—
82C2×D92—41no—
83C2×D92C2×C812yes—
84C2×C4×D23—42no—
85C2×C4×D23—42no—
86C2×C4×D23—42no—
87C2×C8×C23—42no—
88C2×C8×C23—42no—
89C2×C8×C23—42no—
90C42×C23—22no—
91C42×C23—22no—
92C42×C23—41no—
93C42×C23—41no—
94C22⋊Dic23—42no—
95(C2×D23)⋊C4—24no—
96(C2×D23)⋊C4—42no—
97(C2×D23)⋊C4—42no—
98(C2×D23)⋊C4—42no—
99C4⋊Dic23—21no—
100C4⋊Dic23—41no—
101C4⋊Dic23—41no—
102C4⋊Dic23C2×C812yes—
103Dic23⋊C4—42no—
104C4×Dic23—42no—
105C2×C23⋊C8—24no—
106C2×C23⋊C8—42no—
107C2×C23⋊C8—42no—
108#7582—231nomaximal, Sylow
109C23×C23—21no—
110C23×C23—21no—
111C23×C23—21no—
112C23×C23—21no—
113C23×C23—21no—
114C23×C23—21no—
115C23×C23C22⋊C812yes—
116C23×C23C2×C22⋊C411yescharacteristic
117C22×D23—22no—
118C22×D23—41no—
119C22×D23—41no—
120C22×D23—41no—
121C22×D23—41no—
122C22×D23—41no—
123C22×D23—41no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23—21no—
132C2×C4×C23—21no—
133C2×C4×C23—21no—
134C2×C4×C23—21no—
135C2×C4×C23—21no—
136C2×C4×C23—42no—
137C2×C4×C23—42no—
138C2×C4×C23—44no—
139C2×C4×C23—44no—
140C2×C4×C23C22⋊C812yes—
141C2×C4×C23#9912yes—
142C2×C4×C23#10412yes—
143C2×C4×C23C22×C811yescharacteristic
144C2×C4×C23C2×M1611yescharacteristic
145C2×C4×C23#13512yes—
146C2×C4×C23AGL(1,ℤ/8)12yes—
147C22⋊D23—48no—
148C2×Dic23—22no—
149C2×Dic23—41no—
150C2×Dic23—41no—
151C2×Dic23—41no—
152C2×Dic23—41no—
153C2×Dic23—41no—
154C2×Dic23—41no—
155C2×Dic23—41no—
156C2×Dic23—41no—
157D92—42no—
158D92—42no—
159C4×D23—84no—
160C8×C23—82no—
161C23⋊C8—44no—
162C4×#121—231no—
163#1817D2311yescharacteristic, complemented
164C4×C22⋊C8—231no—
165#1271—232no—
166#1270—232no—
167C22×C23—22no—
168C22×C23—22no—
169C22×C23—22no—
170C22×C23—41no—
171C22×C23—41no—
172C22×C23—41no—
173C22×C23—41no—
174C22×C23C2×C22⋊C811yescharacteristic
175C22×C23C2×#9911yescharacteristic
176C22×C23#41311yescharacteristic
177C22×C23#41611yescharacteristic
178C22×C23#41811yescharacteristic
179C22×C23C2×#10411yescharacteristic
180C22×C23#42111yescharacteristic
181C2×D23—42no—
182C2×D23—42no—
183C2×D23—42no—
184C2×D23—81no—
185C2×D23—81no—
186C2×D23—81no—
187C2×D23—81no—
188C4×C23—21no—
189C4×C23—21no—
190C4×C23—22no—
191C4×C23—22no—
192C4×C23—22no—
193C4×C23—22no—
194C4×C23—22no—
195Dic23—42no—
196Dic23—81no—
197Dic23—81no—
198C2×#121—231no—
199C2×C4×D4—231no—
200C2×C4×D4—461no—
201C22×C42C2×D2311yescharacteristic
202C2×C22⋊C8—21no—
203C2×C22⋊C8—461no—
204C2×C4×C8—461no—
205#390—231no—
206#389—231no—
207#388—461no—
208#386—461no—
209#380—231no—
210C4×C4⋊C4—231no—
211C4×C22⋊C4—461no—
212#336—21no—
213#336—232no—
214#336C2×D2312yes—
215C2×C23—42no—
216C2×C23#145911yescharacteristic
217C2×C23#147611yescharacteristic
218C2×C23#147811yescharacteristic
219C2×C23#150711yescharacteristic
220C2×C23#151611yescharacteristic
221C2×C23#152911yescharacteristic
222C2×C23#155311yescharacteristic
223D23—82no—
224C22×D4—231no—
225C22×D4—461no—
226C23×C4—461no—
227C23×C4C4×D2311yescharacteristic
228C23×C4D9211yescharacteristic
229C23×C4C22⋊D2311yescharacteristic
230C22×C8—22no—
231C22×C8—462no—
232#121—234no—
233#121—462no—
234C4×D4—922no—
235C4×D4—924no—
236C2×C4⋊C4—231no—
237C2×C4⋊C4—231no—
238C2×C4⋊C4—231no—
239C2×C4⋊C4—461no—
240C2×C22⋊C4—461no—
241C2×C22⋊C4—461no—
242C2×C22⋊C4—461no—
243C2×C22⋊C4—461no—
244C2×C22⋊C4—461no—
245C2×C42—42no—
246C2×C42—461no—
247C2×C42C4×D2311yescharacteristic
248C2×C42D9211yescharacteristic
249C2×C42C22⋊D2311yescharacteristic
250C2×C42C22×D2311yescharacteristic
251C22⋊C8—42no—
252C22⋊C8—464no—
253C4×C8—922no—
254#95—461no—
255#95—461no—
256#95—461no—
257C23#758211yescharacteristic, complemented, Sylow
258C24—461no—
259C24(C2×D23)⋊C411yescharacteristic
260C2×D4—232no—
261C2×D4—464no—
262C2×D4—461no—
263C2×D4—921no—
264C2×D4—921no—
265C2×D4—922no—
266C2×D4—922no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—461no—
276C22×C4—461no—
277C22×C4—461no—
278C22×C4—922no—
279C22×C4—922no—
280C22×C4—922no—
281C22×C4C8×D2312yes—
282C22×C4#6726212yes—
283C22×C4(C2×D23)⋊C411yescharacteristic
284C22×C4(C2×D23)⋊C411yescharacteristic
285C22×C4(C2×D23)⋊C411yescharacteristic
286C22×C4C2×C4×D2311yescharacteristic
287C22×C4C2×D9211yescharacteristic
288C22×C4C2×C22⋊D2311yescharacteristic
289C2×C8—42no—
290C2×C8—42no—
291C2×C8—42no—
292C2×C8—464no—
293C2×C8—922no—
294C2×C8—922no—
295C4⋊C4—232no—
296C4⋊C4—461no—
297C4⋊C4—921no—
298C4⋊C4—921no—
299C4⋊C4—922no—
300C22⋊C4—464no—
301C22⋊C4—922no—
302C22⋊C4—922no—
303C22⋊C4—922no—
304C22⋊C4—922no—
305C42—22no—
306C42—22no—
307C42—41no—
308C42—41no—
309C42—922no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—462no—
317C23—921no—
318C23—921no—
319C23—921no—
320C23—921no—
321C23—921no—
322C23—921no—
323C23(C2×D23)⋊C812yes—
324C23C2×(C2×D23)⋊C411yescharacteristic
325D4—922no—
326D4—922no—
327D4—928no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—462no—
345C2×C4—921no—
346C2×C4—921no—
347C2×C4—921no—
348C2×C4—921no—
349C2×C4—921no—
350C2×C4—921no—
351C2×C4—921no—
352C2×C4—921no—
353C2×C4—1844no—
354C2×C4#1062498812yes—
355C2×C4(C2×D23)⋊C812yes—
356C2×C4#1062500712yes—
357C2×C4C2×C8×D2311yescharacteristic
358C2×C4C2×#6726211yescharacteristic
359C2×C4#1062507912yes—
360C2×C4#1062512112yes—
361C8—82no—
362C8—924no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—922no—
371C22—922no—
372C22—922no—
373C22—1841no—
374C22—1841no—
375C22—1841no—
376C22—1841no—
377C22C2×(C2×D23)⋊C811yescharacteristic
378C22C2×#1062498811yescharacteristic
379C22#1309239911yescharacteristic
380C22#1309241111yescharacteristic
381C22#1309242311yescharacteristic
382C22C2×#1062500711yescharacteristic
383C22#1309243511yescharacteristic
384C4—22no—
385C4—22no—
386C4—22no—
387C4—22no—
388C4—21no—
389C4—21no—
390C4—22no—
391C4—922no—
392C4—1841no—
393C4—1841no—
394C2—42no—
395C2—1842no—
396C2#1567171311yescharacteristic
397C2#1567177711yescharacteristic
398C2#1567178911yescharacteristic
399C2#1567191411yescharacteristic
400C2#1567195111yescharacteristic
401C2#1567200511yescharacteristic
402C2#1567210311yescharacteristic
subgroupG/H
centerC23C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C8
FrattiniC2×C42C22×D23
FittingC23×#1817C2
socleC23×C23C2×C22⋊C4
hypercenter#1817D23
hypocenterC23#7582
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C4×C22⋊(C23⋊C8)C2semidirect
3. #15671219C2semidirect
4. #15671217C2semidirect
5. C23×#1817C2semidirect
37. #10625101C8semidirect
163. #1817D23semidirect
257. C23#7582semidirect